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Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
Analysis of credibility is a reverse-Bayes technique that has been proposed by Matthews (2001) to overcome some of the shortcomings of significance tests. A significant result is deemed credible if current knowledge about the effect size is…
The logical and practical difficulties associated with research interpretation using P values and null hypothesis significance testing have been extensively documented. This paper describes an alternative, likelihood-based approach to…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…
This paper raises concerns about the advantages of using statistical significance tests in research assessments as has recently been suggested in the debate about proper normalization procedures for citation indicators. Statistical…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
It is proposed to define "quantumness" of a system (micro or macroscopic, physical, biological, social, political) by starting with understanding that quantum mechanics is a statistical theory. It says us only about probability…
Statisticians usually restrict regression to model relationships that are explicitly defined dependent and independent random variables; this paper outlines the newly developed method of non-response analysis and rotational analysis for…
Which type of statistical uncertainty -- statistical (in)significance with a p-value, or a Bayesian probability -- enables people to see the continuous nature of uncertainty more clearly in a policymaking context? An original survey…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
We introduce a method for calculating \(p\)-values to test causal hypotheses in qualitative research \emph{a la} process tracing. As in an experiment, our \(p\)-value tells us how often one would make the same or more compelling…
This chapter demystifies P-values, hypothesis tests and significance tests, and introduces the concepts of local evidence and global error rates. The local evidence is embodied in \textit{this} data and concerns the hypotheses of interest…
Statistical thinking partially depends upon an iterative process by which essential features of a problem setting are identified and mapped onto an abstract model or archetype, and then translated back into the context of the original…
There is a general agreement that it is important to consider the practical relevance of an effect in addition to its statistical significance, yet a formal definition of practical relevance is still pending and shall be provided within…
P-values are widely used in both the social and natural sciences to quantify the statistical significance of observed results. The recent surge of big data research has made the p-value an even more popular tool to test the significance of…
A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the $L_{2}$-contrast function and a simple…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…